Question

The mass of a hydrogen molecule is $3.32\times {10}^{-27}\text{kg}.$ ${10}^{23}$ hydrogen molecules strike per second on a fixed wall of area $2{\text{cm}}^2$ at an angle of ${45}^{\circ }$ to the normal. They rebound elastically with a speed of ${10}^3\text{m/s}$, then the pressure on the wall is nearly,

• A. $2.35\times {10}^2{\text{N/m}}^2$
• B. $4.70\times {10}^2{\text{N/m}}^2$
• C. $2.35\times {10}^3{\text{N/m}}^2$
• D. $4.70\times {10}^3{\text{N/m}}^2$

Answer 1

The correct option is C $2.35\times {10}^3{\text{N/m}}^2$


Change in momentum per collision
$=2mV\cos \theta$
$=mV\sqrt{2}$, as $\theta ={45}^{\circ }$
Now, change in momentum per second
$=$ Average normal force on wall
$=mV\sqrt{2}\times {10}^{23}\text{N}$

$\text{Pressure}=\frac{\text{Normal force}}{\text{Area}}$

$=\frac{mV\sqrt{2}}{2\times {10}^{-4}}\times {10}^{23}$

$=\frac{\sqrt{2}\times 3.32\times {10}^{-27}\times {10}^3\times {10}^{23}}{2\times {10}^{-4}}$

$=2.35\times {10}^3{\text{N/m}}^2$

Hence, $\left(C\right)$ is the correct answer.